An immune system–tumour interactions model with discrete time delay: Model analysis and validation

• A generalised immune system–tumour interactions model with time delay is proposed.
• The mathematical properties and model dynamic are analytically studied.
• Model is validated with the sets of the experimental data.
• The biological conclusions are formulated.

In this article a generalised mathematical model describing the interactions between malignant tumour and immune system with discrete time delay incorporated into the system is considered. Time delay represents the time required to generate an immune response due to the immune system activation by cancer cells. The basic mathematical properties of the considered model, including the global existence, uniqueness, non-negativity of the solutions, the stability of steady sates and the possibility of the existence of the stability switches, are investigated when time delay is treated as a bifurcation parameter. The model is validated with the sets of the experimental data and additional numerical simulations are performed to illustrate, extend, interpret and discuss the analytical results in the context of the tumour progression.